Hallucinations in SPT-based reasoning models manifest as topological defects (e.g., vortices or domain walls) in the model's internal order parameter field, allowing for intrinsic, unsupervised error detection.

Motivation

If correct reasoning is a symmetry-protected phase, then logical errors should theoretically correspond to local symmetry-breaking events or topological defects. This implies that hallucinations could be detected not by checking the output, but by measuring the 'winding number' or topological charge of the activation landscape.

Proposed Method

Train the SPT-based architecture on the symbolic tasks described in the paper. Introduce noise to induce errors. developing a diagnostic tool that calculates local topological invariants (e.g., Chern numbers) on the attention maps or hidden states during inference. Correlate non-trivial topological charges with incorrect outputs.

Expected Contribution

A physics-grounded, unsupervised metric for confidence that is theoretically distinct from (and potentially superior to) probabilistic uncertainty or log-probs.

Required Resources

High-level expertise in topological physics and deep learning interpretability; the codebase from the original paper.

Source Paper

Robust Reasoning as a Symmetry-Protected Topological Phase

View Paper Details →